Capacitor and energy conservation

[spacetime]

Say, you have a parallel plate ideal capacitor and you choose a rectangular path, one side of which lies inside the region of electric field and the side parallel to that lies outside it.
The other two sides are obviously perpendicular to the field.

If I take this rectangular path then how is the line integral along this path zero. Because it is positive for one path and zero for three others.
What is wrong here?
The line integral must be zero for conservation of energy.


spacetime
www.geocities.com/physics_all/index.html

 

[Atheist]

The E-field you are probably having in mind is for an ideal plate capacitor with the plates being (infinitely expanded) planes. Thus, your parallel path lying outside the E-field doesn´t exist.
If, on the other hand, you consider finite plates your E-field becomes more complicated and thus your assumtions on the integrals (two lines being perpendicular to the field) are not true.

 

[reilly]

Try this: the field is perpendicular to the plate. So, the line integrals along the two segments perpendicular to the plate cancel out. Note, this particular problem is often used to illustrate the various integral relations governing the eletric field.

(Clearly, the integrals along the paths parallel to the capacitor plate are zero. All of this, of course, says that the electric potential exists, and, given a zero point, is unique, conservative, and path independent.)

Regards,
Reilly Atkinson